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If S(1), S(2), S(3),…., S(n) are the sum...

If `S_(1), S_(2), S_(3),…., S_(n)` are the sums to infinity of n infinte geometric series whose first terms are 1,2,3,… n and whose common ratios are `(1)/(2), (1)/(3), (1)/(4), ….(1)/(n+1)` respectively, show that, `S_(1) + S_(2) + S_(3) +…S_(n) = (1)/(2)n(n+3)`

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